Few people die under circumstances that allow their organs to be successfully donated. In the UK, the number of such deaths has fallen by 3% in 2014 compared to a year ago. That means, for the first time in a decade, the number of people who could donate their organs has fallen, too.

For someone to become a potential organ donor, the person has to be declared brain dead (or assumed to have no other way to recover) while their body is kept on a ventilator. In such a situation, after...